Optimal Control of Distributed-Parameter Systems based on Differentiable Orthogonal Functions

Keywords

Abstract

Taking the advantages of the properties of the
differentiability of differentiable orthogonal functions,
such as the Chebyshev function sequences, we can apply
differential operation matrices, instead of the
corresponding integral operation matrices, to the solution
of the optimal control of distributed-parameter systems.
The advantage of this method is that we can solve the
optical control problems through differential operations
and obtain an analytical linear presentation of the optimal
solutions. As we know, the operation process based on the
method of integral operations for solving such problems is
quite sophisticated and tedious. The method based on
differentiable orthogonal functions presented in this paper
can greatly simplify the solution process and avoid such
complex work and the solution results are quite
satisfactory. The proposed method of the differentiable
function sequences approach for the solution in this paper
avoids tedious integral operations and is characterized by
directness and feasibility.